Navigating local minima and bifurcations in brittle thin film systems with irreversible damage
(2025) In Computer Methods in Applied Mechanics and Engineering 445.- Abstract
We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to algorithmic choices. In this paper, we inquire into the effectiveness of quasi-Newton algorithms as an alternative to conventional Newton-Raphson solvers. These algorithms improve convergence by constructing a positive definite approximation of the Hessian, trading improved convergence for the risk of missing bifurcation points and stability thresholds. In the absence of irreversibility constraints, we construct an equilibrium map that represents all stable and unstable equilibrium states as a function of... (More)
We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to algorithmic choices. In this paper, we inquire into the effectiveness of quasi-Newton algorithms as an alternative to conventional Newton-Raphson solvers. These algorithms improve convergence by constructing a positive definite approximation of the Hessian, trading improved convergence for the risk of missing bifurcation points and stability thresholds. In the absence of irreversibility constraints, we construct an equilibrium map that represents all stable and unstable equilibrium states as a function of the external load, using well-known branch-following bifurcation techniques. Our main finding is that quasi-Newton algorithms fail to select stable evolution paths without exact second variation information. To overcome this, we introduce a spectral stability criterion based on the full Hessian, which enables the identification of optimal perturbations and improves path-following accuracy. We then extend our analysis to the irreversible case, where admissible perturbations are constrained to a cone. We develop a nonlinear constrained eigenvalue solver to compute the minimal eigenmode within this restricted space and show that it plays a key role in distinguishing physical instabilities from numerical artifacts. Our results provide practical guidance for robust computation of fracture paths in irreversible, non-convex settings.
(Less)
- author
- Terzi, M. M. ; Salman, O. U. LU ; Faurie, D. and León Baldelli, A. A.
- organization
- publishing date
- 2025-10
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Bifurcation, Convex-cone, Evolution, Fracture, Irreversibility, Stability
- in
- Computer Methods in Applied Mechanics and Engineering
- volume
- 445
- article number
- 118201
- publisher
- Elsevier
- external identifiers
-
- scopus:105010838074
- ISSN
- 0045-7825
- DOI
- 10.1016/j.cma.2025.118201
- language
- English
- LU publication?
- yes
- id
- 34987151-b4d5-4714-911c-a8f53328c830
- date added to LUP
- 2025-10-29 15:44:00
- date last changed
- 2025-10-29 15:44:49
@article{34987151-b4d5-4714-911c-a8f53328c830,
abstract = {{<p>We investigate the computation of stable fracture paths in brittle thin films using one-dimensional damage models with an elastic foundation. The underlying variational formulation is non-convex, making the evolution path sensitive to algorithmic choices. In this paper, we inquire into the effectiveness of quasi-Newton algorithms as an alternative to conventional Newton-Raphson solvers. These algorithms improve convergence by constructing a positive definite approximation of the Hessian, trading improved convergence for the risk of missing bifurcation points and stability thresholds. In the absence of irreversibility constraints, we construct an equilibrium map that represents all stable and unstable equilibrium states as a function of the external load, using well-known branch-following bifurcation techniques. Our main finding is that quasi-Newton algorithms fail to select stable evolution paths without exact second variation information. To overcome this, we introduce a spectral stability criterion based on the full Hessian, which enables the identification of optimal perturbations and improves path-following accuracy. We then extend our analysis to the irreversible case, where admissible perturbations are constrained to a cone. We develop a nonlinear constrained eigenvalue solver to compute the minimal eigenmode within this restricted space and show that it plays a key role in distinguishing physical instabilities from numerical artifacts. Our results provide practical guidance for robust computation of fracture paths in irreversible, non-convex settings.</p>}},
author = {{Terzi, M. M. and Salman, O. U. and Faurie, D. and León Baldelli, A. A.}},
issn = {{0045-7825}},
keywords = {{Bifurcation; Convex-cone; Evolution; Fracture; Irreversibility; Stability}},
language = {{eng}},
publisher = {{Elsevier}},
series = {{Computer Methods in Applied Mechanics and Engineering}},
title = {{Navigating local minima and bifurcations in brittle thin film systems with irreversible damage}},
url = {{http://dx.doi.org/10.1016/j.cma.2025.118201}},
doi = {{10.1016/j.cma.2025.118201}},
volume = {{445}},
year = {{2025}},
}